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Ionization feedback should impact the probability distribution function (PDF)of the column density around the ionized gas. We aim to quantify this effectand discuss its potential link to the Core and Initial Mass Function (CMF/IMF).We used in a systematic way Herschel column density maps of several regionsobserved within the HOBYS key program: M16, the Rosette and Vela C molecularcloud, and the RCW 120 H ii region. We fitted the column density PDFs of allclouds with two lognormal distributions, since they present a double-peak orenlarged shape in the PDF. Our interpretation is that the lowest part of thecolumn density distribution describes the turbulent molecular gas while thesecond peak corresponds to a compression zone induced by the expansion of theionized gas into the turbulent molecular cloud. The condensations at the edgeof the ionized gas have a steep compressed radial profile, sometimesrecognizable in the flattening of the power-law tail. This could lead to anunambiguous criterion able to disentangle triggered from pre-existing starformation. In the context of the gravo-turbulent scenario for the origin of theCMF/IMF, the double peaked/enlarged shape of the PDF may impact the formationof objects at both the low-mass and the high-mass end of the CMF/IMF. Inparticular a broader PDF is required by the gravo-turbulent scenario to fitproperly the IMF with a reasonable initial Mach number for the molecular cloud.Since other physical processes (e.g. the equation of state and the variationsamong the core properties) have already been suggested to broaden the PDF, therelative importance of the different effects remains an open question.

Ionization compression impact on dense gas distribution and star formation, Probability density functions around H ii regions as seen by Herschel